Math, asked by paragc3, 8 months ago

if x = 4 - √ 5 find the value of x2+1/x2

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Answers

Answered by vickylucky6
7

Answer:

\begin{gathered}x = 9 - 4 \sqrt{5} \\ \\ \frac{1}{x} = \frac{1}{9 - 4 \sqrt{5} } \\ \\ \frac{1}{x} = \frac{1}{9 - 4 \sqrt{5} } \times \frac{9 + 4 \sqrt{5} }{9 + 4 \sqrt{5} } \\ \\ \frac{1}{x} = \frac{9 + 4 \sqrt{5} }{ {(9)}^{2} - {(4 \sqrt{5} )}^{2} } \\ \\ \frac{1}{x} = \frac{9 + 4 \sqrt{5} }{81 - 80} \\ \\ \frac{1}{x} = 9 + 4 \sqrt{5}\end{gathered}x=9−45x1=9−451x1=9−451×9+459+45x1=(9)2−(45)29+45x1=81−809+45x1=9+45

Now,

\begin{gathered}{x}^{2} + \frac{1}{ { x}^{2} } = {(9 - 4 \sqrt{5}) }^{2} + {(9 + 4 \sqrt{5} )}^{2} \\ \\ = 81 + 80 - 72 \sqrt{5} + 81 + 80 + 72 \sqrt{5} \\ \\ = 81 + 80 + 81 + 80 \\ \\ = 161 + 161 \\ \\ = 322\end{gathered}x2+x21=(9−45)2+(9+45)2=81+80−725+81+80+725=81+80+81+80=161+161=322

Step-by-step explanation:

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